Question
x squared minus 7 x minus 10 equals negative 2 x minus 4
Answers
GPT-4o mini
To solve the equation \( x^2 - 7x - 10 = -2x - 4 \), let's first bring all terms to one side of the equation so that it equals zero.
1. Start by adding \( 2x \) and \( 4 \) to both sides of the equation:
\[
x^2 - 7x - 10 + 2x + 4 = 0
\]
2. Combine like terms:
\[
x^2 - 5x - 6 = 0
\]
Now we can factor the quadratic equation \( x^2 - 5x - 6 \):
3. To factor, we need two numbers that multiply to \(-6\) and add up to \(-5\). These numbers are \(-6\) and \(1\).
\[
(x - 6)(x + 1) = 0
\]
4. Now set each factor equal to zero:
\[
x - 6 = 0 \quad \text{or} \quad x + 1 = 0
\]
5. Solve for \( x \):
\[
x = 6 \quad \text{or} \quad x = -1
\]
Thus, the solutions to the equation are:
\[
x = 6 \quad \text{and} \quad x = -1
\]
1. Start by adding \( 2x \) and \( 4 \) to both sides of the equation:
\[
x^2 - 7x - 10 + 2x + 4 = 0
\]
2. Combine like terms:
\[
x^2 - 5x - 6 = 0
\]
Now we can factor the quadratic equation \( x^2 - 5x - 6 \):
3. To factor, we need two numbers that multiply to \(-6\) and add up to \(-5\). These numbers are \(-6\) and \(1\).
\[
(x - 6)(x + 1) = 0
\]
4. Now set each factor equal to zero:
\[
x - 6 = 0 \quad \text{or} \quad x + 1 = 0
\]
5. Solve for \( x \):
\[
x = 6 \quad \text{or} \quad x = -1
\]
Thus, the solutions to the equation are:
\[
x = 6 \quad \text{and} \quad x = -1
\]